Two-dimensional biphenylene: a promising anchoring material for lithium-sulfur batteries

Trapping lithium polysulfides (LiPSs) on a material effectively suppresses the shuttle effect and enhances the cycling stability of Li–S batteries. For the first time, we advocate a recently synthesized two-dimensional material, biphenylene, as an anchoring material for the lithium-sulfur battery. The density functional theory calculations show that LiPSs bind with pristine biphenylene insubstantially with binding energy ranging from −0.21 eV to −1.22 eV. However, defect engineering through a single C atom vacancy significantly improves the binding strength (binding energy in the range −1.07 to −4.11 eV). The Bader analysis reveals that LiPSs and S8 clusters donate the charge (ranging from −0.05 e to −1.12 e) to the biphenylene sheet. The binding energy of LiPSs with electrolytes is smaller than those with the defective biphenylene sheet, which provides its potential as an anchoring material. Compared with other reported two-dimensional materials such as graphene, MXenes, and phosphorene, the biphenylene sheet exhibits higher binding energies with the polysulfides. Our study deepens the fundamental understanding and shows that the biphenylene sheet is an excellent anchoring material for lithium-sulfur batteries for suppressing the shuttle effect because of its superior conductivity, porosity, and strong anchoring ability.


Results and discussion
The BPN sheet possesses a carbon lattice with a rectangular primitive unit cell formed by six C atoms having tetragon, hexagon, and octagon rings. The optimized lattice constants of the BPN sheet are 4.51 Å and 3.76 Å, consistent with the previous study 24 . The electron localization function along the (0 0 1) plane shows the underlying characteristics of C-C bonds (see Fig. 1b) and confirms that a large proportion of bonds in the BPN sheet are strong covalent bonds. In Fig. 1b, the red color shows intense localization and, in turn, a stronger bond. As illustrated in Fig. 1a, there are eight different adsorption sites. The S1, S2, and S3 sites are the octagon, tetragon, and hexagon hollows, respectively, and the S4, S5, and S6 sites are the distinctive bridges between the carbon atoms, and S7, S8 which are randomly chosen carbon atoms. Since lattice defects are inevitable during the synthesis process, the bindings of LiPSs and S 8 are also investigated on the defective BPN sheet having a single C vacancy. Such defects can also be generated using a laser/electron beam of an appropriate energy bombardment 28 . There are two distinctive carbon atoms in the BPN sheet (marked with two dotted circles in Fig. 1a and named them D1 and D2, respectively), leading to two distinctive single vacancy defects. The structures with the single defect are illustrated in Fig. 1c-f combined with their respective electron localization function plots. In both cases, intense red color is noticed at the vacancy site, indicating a free electron (dangling bond), which directly affects the bonding of polysulfides with the BPN sheet. In addition, the defective BPN sheets exhibit a magnetic moment of a value of 1 μ B in both D1 and D2 cases, which is directly reflected in the calculated density of states. Compared to pristine BPN, the defective BPN sheets DOS is asymmetrical, which can be explained by the fact that when a vacancy has created the relaxation of its nearest neighbor atoms and resulting charge redistribution saturate the orbitals of two of the three C atoms, and the remaining unsaturated carbon atom is responsible for the magnetic moment. The computed density of states of pristine BPN and defective sheets are available in the supplementary information (SI) (see Fig. S2). Figure S2 shows that the biphenylene sheet is metallic, resulting in better anchoring material than phosphorene. Much higher performance as an anchoring material is expected of its porous nature compared to graphene and MXene.
The strength of the chemical bond in the defective BPN sheet is investigated with the aid of the projected crystal-orbital Hamilton population (-pCOHP) method, in which -pCOHP is divided into bonding and antibonding states, as shown in Fig. 2. In both cases, minor antibonding states near the Fermi level are observed, related to the electronic structure distortion resulting from the lone electron pair, making the two spin sublattices inequivalent. Apart from the minor antibonding, the C-C bonds contribute to the chemical stability of the bonding region. All the filled bands below the Fermi level contribute to chemical stability.
As cathode discharge, polysulfides significantly influence the capacity and cycling stability of Li-S batteries. The optimized most stable molecular structure of Li 2 S x (x = 1, 2, 4, 6, 8) and S 8 clusters are shown in the supplementary information (Fig. S3 in SI). The Li-S bond is more extended than the S-S bond, indicating that as the number of sulfur atoms increases, the high-order LiPSs can easily be ionized as Li + and polysulfide anions, resulting in the so-called shuttle effect 9 . The binding energy of the LiPSs and S 8 clusters with the BPN sheet is calculated by considering the most stable adsorption configuration ( Fig. S1 in SI). Among the eight different adsorption sites, in most cases, LiPSs preferred to adsorb near the C-C bond of the octagon ring (S6 site in Fig. 1) because of charge accumulation. The maximum binding energy is −1.22 eV for Li 2 S, whereas the minimum binding energy of −0.43 eV is obtained for Li 2 S 4 .
The binding energy decreases gradually with the increase of the S atoms, but it also differs with the orientations of the molecule. When the S atom increased to 2 in Li 2 S 2 , the binding energy decreased by 0.342 eV because of the conformational changes noticed in the relaxed configurations. Two lithium atoms of Li 2 S are facing toward the sheet compared to only one lithium atom in Li 2 S 2 , directly resulting in lower binding energy. The highest binding energy values for each cluster with the corresponding favorable adsorption site are listed in Table 1, and the binding energy for each site is presented in the SI (see Fig S4), which ensures the stability of LiPSs on the BPN sheet. However, the binding energy values for the x > 3 are low and need further improvement. The binding energy of polysulfides is enhanced with defected BPN sheet. All the polysulfide clusters are placed at the top of the defect, and then the structures are relaxed, as shown in Figs. 3 and 4. The single C vacancy shows high charge localization (Fig. 1), shared with the Li 2 S x and S 8 clusters, resulting in higher binding energy than the pristine BPN sheet. For all Li 2 S x clusters except with Li 2 S 6 in defected BPN sheet, two Li atoms lie nearest to the surface. www.nature.com/scientificreports/   The leading cause of the shuttle effect in Li-S batteries is the smaller binding energy of LiPSs and S 8 clusters with the cathode surface than with the electrolyte. Therefore, dissolution in the electrolytes and diffusion to the anode of LiPSs is easy. The binding energies of LiPSs with (1,3-dioxolane (DOL) and 1,2-dimethoxyethane (DME)) electrolytes are calculated. The binding energies of LiPSs with graphene are also listed to gain a more profound sense of BPN sheet as an anchoring material. The binding energies of LiPSs with DME and DOL molecules are smaller than those with the defected BPN sheet and higher than those with graphene, which indicates that graphene could not effectively trap LiPSs, but the defected BPN sheet can effectively trap LiPSs. Compared Table 1. Binding energies (in eV) of LiPSs and S 8 clusters with pristine BPN (favorable adsorption site), defective BPN sheet, DOL, DME, and graphene.   30 ), the binding energy of LiPSs with the defected BPN sheet is more substantial, which indicates that the BPN sheet is indeed a promising anchoring material. Defected BPN sheet outperforms the pristine sheet in the binding energy of LiPSs and S 8 clusters. The Bader analysis shows that the LiPSs and S 8 donate the charge of between −0.05 e to −1.02 e to the BPN sheet (see Table 2). The charge is mainly accumulated (depleted) on S (Li) before absorption and transferred substantially to the sheet after absorption of clusters. The charge density difference between LiPSs and the defective BPN sheet is calculated according to �ρ = ρ total − ρ defectiveBPN − ρ LiPSs/S 8 , where ρ total , ρ defectiveBPN , and ρ LiPSs/S 8 are the calculated charge density of combined BPN sheet and LiPSs/S 8 systems, defected BPN sheet alone, and the isolated LiPSs/S 8 clusters, respectively. The calculated charge density difference of the defective BPN sheet is shown in Figs. 5 and 6. Figure 5 shows, Li 2 S 6 has the least apparent charge redistribution compared to the other clusters. For Li 2 S x (x = 1, 2, 4, 8) and S 8 adsorption, electrons are mainly accumulated in the region between Li and S nearest. The

Conclusion
In summary, the density functional theory calculations are carried out to explore the potential and performance of 2D BPN sheet as an anchoring material for Li-S batteries. The results show that the defective BPN sheet significantly improves the binding of LiPSs with binding energies ranging from −1.07 to −4.11 eV, which can effectively inhibit the shuttle effect and reduce the migration barrier to realize the rapid realization charge/discharge. The Bader charge analysis shows an electronic charge transfer ranging from −0.05 e to −1.12 e from LiPSs to the BPN sheet. Compared to graphene, MXenes, and other potential anchoring materials, the BPN sheet has the highest binding energies, making it a more efficient and reliable choice. Our work deepens the fundamental  www.nature.com/scientificreports/ understanding of the anchoring mechanism and demonstrate that the biphenylene sheet has excellent potential to be an outstanding anchoring material for Li-S batteries for suppressing the shuttle effect.

Data availability
No datasets were generated or analysed during the current study.